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Life sciences · Preprint
arXiv · September 3, 2026
Raises a question worth testing. It does not answer one.
This is an unpublished theoretical contribution presenting a PAC learning algorithm for general-sum concurrent stochastic games with transition uncertainty. The framework provides a principled approach to computing approximate Nash equilibria while certifying non-existence, with polynomial sample complexity guarantees. The work is foundational in machine learning theory but has not yet been peer reviewed and remains at the stage of algorithm design and proof-of-concept empirical validation.
Theoretical algorithmic framework with proof-of-concept empirical validation on benchmarks. Intervention: PAC learning algorithm for concurrent stochastic games with transition uncertainty, using robust MDP-based exploration and Nash margin characterisation.
Algorithm achieves ε-approximate Nash equilibrium with social-welfare value ε-close to optimal or certifies that no exact NE exists Sample complexity bound: Õ(R²ₘₐₓ H⁴ |S|² |A| / (p_reach ε²)) under minimum reachability condition p_reach > 0 Empirical results on benchmark CSGs demonstrate near-optimal performance and sample complexity consistent with theory
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This is a theoretical computer science contribution presenting a novel algorithmic framework with mathematical guarantees, not an empirical clinical or translational study; it advances understanding of learning in game-theoretic settings but requires experimental validation and practical implementation.
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We introduce the first Probably Approximately Correct (PAC) learning framework for general-sum concurrent stochastic games (CSGs) with transition uncertainty, while addressing the challenge of Nash equilibrium (NE) existence. Our algorithm maintains data-driven $L^1$ confidence sets over transition kernels and solves a robust CSG to compute a social-welfare optimal $\varepsilon$-NE, using a robust MDP-based exploration mechanism to drive joint state-action coverage. Crucially, we introduce a Nash margin characterisation that enables principled reasoning about equilibrium existence: the framework either returns an $\varepsilon$-approximate NE whose social-welfare value is $\varepsilon$-close to optimal, or provides a sound certificate that no exact NE exists. Under a minimum reachability condition $p_{\mathrm{reach}}>0$ over relevant state-action pairs, the algorithm terminates after a polynomial number of trajectory samples, with sample complexity $\widetilde{O}\left( {R_{\max}^2 H^4 |S|^2 |A| / (p_{\mathrm{reach}} \varepsilon^2)} \right)$. Empirical results on benchmark CSGs demonstrate near-optimal performance, correct handling of equilibrium (non-)existence, and sample complexity consistent with theory.
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